Quantum Field Theory 2
Code  Completion  Credits  Range  Language 

02KTPE2  Z,ZK  5  3+1  Czech 
 Lecturer:
 Tutor:
 Supervisor:
 Department of Physics
 Synopsis:

Symmetries, gauge fields, spontaneous symmetry breaking, quantization of relativistic fields, reduction formulas for Smatrix elements, perturbative series, Wick theorem, radiative corrections, renormalization.
 Requirements:

Knowledge of the basic course of physics, quantum physics and Quantum field theory 1 lecture
 Syllabus of lectures:

1. Lagrange formalism for free fields, symmetries and Noether theorem, spacetime symmetries.
2. Gauge symmetries, nonabelian transformations, YoungMills fields
3. Axial transformation, sigma model. Spontaneous symmetry breaking, Wigner and Goldstone modes. Explicit symmetry breaking.
4. Free scalar field, canonical commutator relations. Creation and annihilation operators, Hamiltonian, momentum and charge operators. Normal ordering, Fock space. Timeordered products, Feynman propagator and microcausality.
5. Localized states, localized energy densities, vacuum fluctuations.
6. Quantization of free Dirac field.
Vector fields.
7. Interacting fields, (anti)commutation relations. Lehmann spectral decomposition, YoungBaxter equations.LSZ reduction formulas.
8. Perturbation series, Wick theorem, Feynman rules.
9. Several processes in tree approximation.
10. Diagrams with loops: selfenergy, vacuum polarization.
11. Renormalization  general principles.
12. Renormalization of QED in oneloop.
 Syllabus of tutorials:

1. Gauge symmetries, nonabelian transformations, YoungMills fields
2. Axial transformation, sigma model. Explicit symmetry breaking.
3. Creation and annihilation operators, Hamiltonian, momentum and charge operators. Normal ordering, Fock space. Timeordered products, Feynman propagator and microcausality.
4. Localized states, localized energy densities, vacuum fluctuations.
5. Interacting fields, (anti)commutation relations. Perturbation series, Wick theorem, Feynman rules.
6.Several processes in tree approximation, diagrams with loops: selfenergy, vacuum polarization.
 Study Objective:

Knowledge:
Symmetry and its violation, field quantization and Smatrix, perturbative expansion, renormalization
Abilities:
Active knowledge of field theory up to a level of oneloop renormalization of quantum electrodynamics
 Study materials:

Key references:
[1] F. Gross: Relativistic Quantum Mechanics and Field Theory, WileyVCH, 1999; chapters 711
[2] J.D. Bjorken, S.D. Drell: Relativistic Quantum Fields, McGrawHill, 1965; chapters 1117
[3] W. Greiner, J. Reinhardt: Field Quantization, Springer, 2008; chapters 4,5, 8 a 9
Recommended references:
[4] M.E. Peskin, D.V. Schroeder: An Introduction To Quantum Field Theory, Westview Press, 1995
[5] D.J. Griffiths: Introduction to Elementary Particles, John Wiley and sons, 1987
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans:

 Experimentální jaderná a částicová fyzika (compulsory course of the specialization)